Preheat oven to 400 with rack in middle. Butter and flour a 9-inch round cake pan.

Whisk together flour, baking powder, baking soda, and salt.

Beat butter and ⅔ cup sugar with an with an electric mixer at medium-high speed until pale and fluffy, about 2 minutes, then beat in vanilla. Add egg and beat well.

At low speed, mix in flour mixture in 3 batches, alternating with buttermilk, beginning and ending with flour, and mixing until just combined.

Spoon batter into cake pan, smoothing top. Scatter blueberries evenly over top and sprinkle with turbinado sugar.

Bake until cake is golden and a wooden pick inserted into center comes out clean, 25 to 30 minutes. Cool in pan 10 minutes, then turn out onto a rack and cool to warm, 10 to 15 minutes more. Invert onto plate.